Landau Levels and Quantum Group

Abstract

We find a quantum group structure in two-dimensional motions of a nonrelativistic electron in a uniform magnetic field and in a periodic potential. The representation basis of the quantum algebra is composed of wavefunctions of the system. The quantum group symmetry commutes with the Hamiltonian and is relevant to the Landau level degeneracy. The deformation parameter $q$ of the quantum algebra turns out to be given by the fractional filling factor $ν=1/m$ ($m$ odd integer).